Finite Group Databasebeta

← Group #94376

Character table — Group #94376

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56
size1111111122224444888888888888888888881616161616161616161616161616161616161616
order12224444224444442222444444448888888844444444444444448888
χ111111111111111111111111111111111111111111111111111111111
χ2111111111111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-11111
χ31111111111111111111111111111-1-1-1-1-1-1-1-111111111-1-1-1-1-1-1-1-1-1-1-1-1
χ41111111111111111111111111111-1-1-1-1-1-1-1-1-1-1-1-1-1-1-1-111111111-1-1-1-1
χ51111111111111111-1-1-1-1-1-1-1-1111111111111iiii−i−i−i−iiiii−i−i−i−i-1-1-1-1
χ61111111111111111-1-1-1-1-1-1-1-1111111111111−i−i−i−iiiii−i−i−i−iiiii-1-1-1-1
χ71111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1iiii−i−i−i−i−i−i−i−iiiii1111
χ81111111111111111-1-1-1-1-1-1-1-11111-1-1-1-1-1-1-1-1−i−i−i−iiiiiiiii−i−i−i−i1111
χ91111-1-1-1-111-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−i11-1-111-1-1ii−i−iii−i−iii−i−i
χ101111-1-1-1-111-1-111-1-111-1-111-1-111-1-1iiii−i−i−i−i-1-111-1-111−i−iii−i−iiiii−i−i
χ111111-1-1-1-111-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii11-1-111-1-1−i−iii−i−iii−i−iii
χ121111-1-1-1-111-1-111-1-111-1-111-1-111-1-1−i−i−i−iiiii-1-111-1-111ii−i−iii−i−i−i−iii
χ131111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−iii−i−i−i−iii-1-11111-1-1−i−iii
χ141111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1iiii−i−i−i−i−i−iiiii−i−i11-1-1-1-111−i−iii
χ151111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiiiii−i−i−i−iii11-1-1-1-111ii−i−i
χ161111-1-1-1-111-1-111-1-1-1-111-1-11111-1-1−i−i−i−iiiii−i−iiiii−i−i-1-11111-1-1ii−i−i
χ17222222222222222222-2-2-2-222-2-2-2-20000000000000000000000000000
χ182222222222222222-2-22222-2-2-2-2-2-20000000000000000000000000000
χ192222-2-2-2-222-2-222-2-22222-2-2-2-2-2-2220000000000000000000000000000
χ202222-2-2-2-222-2-222-2-2-2-2-2-22222-2-2220000000000000000000000000000
χ2122-2-22i−2i2i−2i2-22i−2i2-22i−2i002-22i−2i000000000000001+i−1−i1−i−1+i1−i−1+i1+i−1−i000000000000
χ2222-2-22i−2i2i−2i2-22i−2i2-22i−2i002-22i−2i00000000000000−1−i1+i−1+i1−i−1+i1−i−1−i1+i000000000000
χ2322-2-22i−2i2i−2i2-22i−2i2-22i−2i00-22−2i2i000000000000001−i−1+i−1−i1+i1+i−1−i−1+i1−i000000000000
χ2422-2-22i−2i2i−2i2-22i−2i2-22i−2i00-22−2i2i00000000000000−1+i1−i1+i−1−i−1−i1+i1−i−1+i000000000000
χ2522-2-22i−2i2i−2i2-22i−2i-22−2i2i2-200002i−2i000000000000000000001−i−1+i1+i−1−i1−i−1+i1+i−1−i0000
χ2622-2-22i−2i2i−2i2-22i−2i-22−2i2i2-200002i−2i00000000000000000000−1+i1−i−1−i1+i−1+i1−i−1−i1+i0000
χ2722-2-22i−2i2i−2i2-22i−2i-22−2i2i-220000−2i2i000000000000000000001+i−1−i−1+i1−i−1−i1+i1−i−1+i0000
χ2822-2-22i−2i2i−2i2-22i−2i-22−2i2i-220000−2i2i00000000000000000000−1−i1+i1−i−1+i1+i−1−i−1+i1−i0000
χ2922-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002-2−2i2i000000000000001−i−1+i1+i−1−i1+i−1−i1−i−1+i000000000000
χ3022-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i002-2−2i2i00000000000000−1+i1−i−1−i1+i−1−i1+i−1+i1−i000000000000
χ3122-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00-222i−2i000000000000001+i−1−i−1+i1−i1−i−1+i−1−i1+i000000000000
χ3222-2-2−2i2i−2i2i2-2−2i2i2-2−2i2i00-222i−2i00000000000000−1−i1+i1−i−1+i−1+i1−i1+i−1−i000000000000
χ3322-2-2−2i2i−2i2i2-2−2i2i-222i−2i2-20000−2i2i000000000000000000001+i−1−i1−i−1+i1+i−1−i1−i−1+i0000
χ3422-2-2−2i2i−2i2i2-2−2i2i-222i−2i2-20000−2i2i00000000000000000000−1−i1+i−1+i1−i−1−i1+i−1+i1−i0000
χ3522-2-2−2i2i−2i2i2-2−2i2i-222i−2i-2200002i−2i000000000000000000001−i−1+i−1−i1+i−1+i1−i1+i−1−i0000
χ3622-2-2−2i2i−2i2i2-2−2i2i-222i−2i-2200002i−2i00000000000000000000−1+i1−i1+i−1−i1−i−1+i−1−i1+i0000
χ37444444444444-4-4-4-40000000000000000000000000000000000000000
χ3844444444-4-4-4-4000000000000000022-2-222-2-200000000000000000000
χ3944444444-4-4-4-40000000000000000-2-222-2-22200000000000000000000
χ404444-4-4-4-444-4-4-4-4440000000000000000000000000000000000000000
χ414444-4-4-4-4-4-44400000000000000002i2i−2i−2i−2i−2i2i2i00000000000000000000
χ424444-4-4-4-4-4-4440000000000000000−2i−2i2i2i2i2i−2i−2i00000000000000000000
χ4344-4-44i−4i4i−4i-44−4i4i00000000000000000000000000000000000000002ζ3−2ζ32ζ−2ζ
χ4444-4-44i−4i4i−4i-44−4i4i0000000000000000000000000000000000000000−2ζ32ζ3−2ζ2ζ
χ4544-4-4−4i4i−4i4i-444i−4i00000000000000000000000000000000000000002ζ−2ζ2ζ3−2ζ3
χ4644-4-4−4i4i−4i4i-444i−4i0000000000000000000000000000000000000000−2ζ2ζ−2ζ32ζ3
χ474-4-4444-4-400000000000000002-22-2002i2−2i2002i2−2i200000000000000000000
χ484-4-4444-4-400000000000000002-22-200−2i22i200−2i22i200000000000000000000
χ494-4-4444-4-40000000000000000-22-222i2−2i2002i2−2i20000000000000000000000
χ504-4-4444-4-40000000000000000-22-22−2i22i200−2i22i20000000000000000000000
χ514-4-44-4-44400000000000000002-2-220022−2200−222200000000000000000000
χ524-4-44-4-44400000000000000002-2-2200−22220022−2200000000000000000000
χ534-4-44-4-4440000000000000000-222-222−2200−22220000000000000000000000
χ544-4-44-4-4440000000000000000-222-2−22220022−220000000000000000000000
χ558-88-88i−8i−8i8i000000000000000000000000000000000000000000000000
χ568-88-8−8i8i8i−8i000000000000000000000000000000000000000000000000

Here ζ is a primitive root of unity of order 8 (ζ8 = 1); i = ζ2.